Calculating π by hand

For Pi Day 2016 I tried to calculate π by hand, using an infinite series. It goes ok.

Before you even start:
- Yes, I know π Day requites writing the date MM/DD. By objective measures: the wrong way. I don't care. My love of π is stronger.

CORRECTIONS:
- At 17:23 it should be π/4 not 1/π. That was contamination from the next graphic. (First spotted by Najeeb Sheikh and Jake Trookman.)

Check out y-cruncher:

Calculating pi by weighing a circle:

Calculating pi with a pendulum:

Music by Howard Carter
Design by Simon Wright

MATT PARKER: Stand-up Mathematician

[FourthDerivative]

This is what I thought mathematicians did for a living when I was a kid. Just adding and subtracting giant lists of numbers all day long.

[karlmuster]

My favorite representation is 355/113 = 3.1415929203... It's easy to remember. You start with the first three odd numbers: 135. You double them up: 113355. You split it in the middle: 113/355. Then you take the inverse: 355/113. And there you have it, pi correct to 7 digits.

[ashaydwivedi]

How fascinating, the calculation of pi starts at 3:14

[eddiegaltek]

You have to go down to -1/1583 to get as good an approximation as 22/7.

[timyang]

perfect for my pi memorization contest i could just calculate it on the spot

[kaazmodan]

I really love the idea of a student randomly walking in on this happening, seeing Matt talk to himself and writing on the chalkboard, and then just saying "He's just having one of his "special" days", then walking out without saying anything.

[servalerror]

Uploaded on March 13, not the 14th...classic Parker Square.

[theCodyReeder]

You could multiply it by 2 and get tau. :)

[braylordian]

The best way to find pi is the equation:

1π

[TazPessle]

When i was 6 i thought they made bigger and bigger circles and measured with better and better rulers to find the digits of Pi. XD

[chinareds]

I'm 37 years old, and this is the first time I've ever seen long division done on one line rather than taking up a whole damn page. Wow.

[kurumi]

Archimedes: approximates pi to the second digit with a 96 sided polygon

*Zu Chongzhi: laughs in 24576 sided polygon and 7th digit of pi*

[bungalo]

This really highlights how amazingly precise 22/7 actually is

[asp-uwu]

Another way you can find π:



I wrote a program to calculate π using both the method you did in this video, and the one above, and it turns out the one above gets much closer with many fewer iterations. Great video sir!

[alejrandom]

2:34 POV: you enter an empty classroom and there's a man randomly shouting "chalkboard"

[leocorn]

<get pi from odd fractions> "Oh that's neat. I wonder how that works."
<gets pi from all fractions> "Woah cool, he knows his stuff."
<gets pi from prime numbers> "Okay, can't wait to see how he knows this."
<teleports to a chalkboard> "HE'S A WITCH!!!"

[kevinocta]

I have no idea why, but I could watch this man do basic math for hours. Honestly... it's odd.

[Mdibah]

Mistake #1 (fixed during montage at 13:08): incorrect number of decimal places written for 1/17

Mistake #2 (@ 12:00): The difference of the decimal expansions given for 1 and 1/3 should be 0.66...667. This throws off the 20th decimal place for the rest (meh).

Mistake #3 (visible @13:03): After adding the decimal for 1/13, the partial sum should be 0.820 934 620 934 620 934 62 (vicinity of 7th decimal place on is wrong). This throws off the rest of the calculation.

The ending tally should be 0.760 459 904 732 350 552 78, which gives 3.041 839 618 929 402 211 12 after multiplying by 4. Again, very close---just issues around the 7th and 8th decimal places.

Mad props for carrying out this masochism by hand; I needed to break out a calculator to track down the arithmetic error.

[EpicUltraKingSmizzy]

was this like a secret 'learning how to divide' video? lol

[jackeown]

Python one-liner:

4*sum([(-1.0)**(k)/(2*k+1) for k in range(0, 10, 1)])